I just tested this on my machine (gcc 5.4.0). At -O2, gcc produced normal looking assembly code. At -O3, gcc produced a monstrosity [0] that I don't feel like fully deciphering.

However, from a brief glance, it does not appear to have created a closed form solution. Instead, it contains a single loop:

    .L4:
        addl    $1, %edx
        paddd   %xmm1, %xmm0
        paddd   %xmm2, %xmm1
        cmpl    %edx, %eax
        ja  .L4 

which seems to be using a SIMD instruction (paddd[1]) that adds does 4 32-bit integer additions in parallel.

After this loop, it does some "housekeeping" (read, something I don't understand) before proceeding to an unwound version of the last iterations of the loop:

    leal    4(%rdx), %ecx
    addl    %edx, %eax
    cmpl    %ecx, %edi
    jl  .L2 
    addl    %ecx, %eax
    leal    8(%rdx), %ecx
    cmpl    %ecx, %edi
    ...
    jl  .L2 
    addl    %ecx, %eax
    leal    28(%rdx), %ecx
    cmpl    %ecx, %edi
    jl  .L2
    addl    %ecx, %eax
    addl    $32, %edx
    leal    (%rax,%rdx), %ecx
    cmpl    %edx, %edi
    cmovge  %ecx, %eax
    ret

Where .L2 is just:

    .L2:
        rep ret

I assume that this is just some form of return, but the documentation I could find [2] seems to suggest that rep is a prefix for string operations, which doesn't make sense.

[0]https://pastebin.com/raw/Y55gQG7p

[1] http://x86.renejeschke.de/html/file_module_x86_id_226.html

[2] https://c9x.me/x86/html/file_module_x86_id_279.html